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numbers of 1x2x3, 2x 3x4,..., 2020x 2021x2022 divisible by 2020

Source: 2020 Swedish Mathematical Competition p1

May 1, 2021
number theorydividesdivisible

Problem Statement

How many of the numbers 1⋅2⋅31\cdot 2\cdot 3, 2⋅3⋅42\cdot 3\cdot 4,..., 2020⋅2021⋅20222020 \cdot 2021 \cdot 2022 are divisible by 20202020?
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